Report Number: CS-TR-75-481
Institution: Stanford University, Department of Computer Science
Title: Hybrid difference methods for the initial boundary-value
problem for hyperbolic equations.
Author: Oliger, Joseph E.
Date: February 1975
Abstract: The use of lower order approximations in the neighborhood of
boundaries coupled with higher order interior approximations
is examined for the mixed initial boundary-value problem for
hyperbolic partial differential equations. Uniform error can
be maintained using smaller grid intervals with the lower
order approximations near the boundaries. Stability results
are presented for approximations to the initial
boundary-value problem for the model equation $u_t$ +
${cu}_x$ = O which are fourth order in space and second order
in time in the interior and second order in both space and
time near the boundaries. These results are generalized to a
class of methods of this type for hyperbolic systems.
Computational results are presented and comparisons are made
with other methods.
http://i.stanford.edu/pub/cstr/reports/cs/tr/75/481/CS-TR-75-481.pdf